Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C24 |
| direct product | C23×#1907 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | #121 |
| commutator | C2×C4 | C22×C4×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C2×C23×AGL(1,ℤ/8) | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ G | |
332 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 736 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25)(26,27)(28,29,33,35,32,31,37,40)(30,36,38,43,39,34,41,42);(28,30,37,38,32,39,33,41)(29,34,35,43,31,36,40,42);(25,27)(28,31)(29,32)(30,36)(33,35)(34,39)(37,40)(38,42)(41,43)736 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×#1907, C23×#21003, C23×#21004, … |
| maximal normal subgroup of | C2×C23×#1907, C23×#21003, C23×#21004, … |
| maximal quotient of | C23×#9095, C23×#9097, C23×#9163, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 639);